The Improbability of the Photographic Process
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The recording medium of the silver halide photographic "emulsion" is a suspension in gelatin of precipitated microcrystals, typically consisting of AgBr or Ag(Br,I), and having linear d i m e n s i o n s of a b o u t 0.1 to several microns. These microcrystals are generally treated with various "sensitizers," notably gold and sulfur c o m p o u n d s , which form "sensitivity centers" on the surfaces of the grains, and adsorbed photographic dyes, which extend the photographic response out to the longer wavelengths of the visible. Proper exposure of the emulsion to the optical signal causes the formation, at each exposed sensitivity center, of a microscopic speck of metallic silver. This speck, known as the latent image, has been shown by various techniques (analysis of the statistical effects of various schedules of exposure, computer simulations, and study of the effects of deposition of atomic clusters) to consist of a minimum of three or four silver atoms (not ions). Its significance lies in the fact that, upon subsequent immersion of the film in an appropriate reducing agent, it can catalyze the conversion of the entire AgBr grain into black, metallic silver. This "development" process thus distinguishes those regions of the film that have been exposed to light from those that have not, with a resulting amplification of the recorded optical signal by a factor of 108 - 109. The grey tones of a photograph result from the statistical distribution of these developed grains. The high sensitivity of photographic films is d u e b o t h to this very great
amplification factor a n d also to the unexpectedly high quantum efficiency of latent image formation. The basic model for the mechanism of this formation was proposed over half a century ago by Gurney and Mott, and has been e x t e n s i v e l y e l u c i d a t e d since t h e n . Absorption of a quantum of energy sufficient to lift an electron into the conduction band results ultimately in trapping that electron at a surface site, whereupon the arrival of an interstitial silver ion produces a silver atom. Subsequent operation of this cycle ultimately forms the three- or four-atom speck which serves as the latent image. O n e can think of m a n y processes which could reduce the efficiency of this cycle: recombination of electrons and holes, electron trapping in the interior of the grain (which is inaccessible to the s t a n d a r d p h o t o g r a p h i c developers), insufficient speed of the ion migration step, or inefficient use of photoelectrons as a result of nucleation of more than one silver speck per grain. Nevertheless, in m o d e r n photographic emulsions, absorption by a microcrystal of only 8 - 1 0 photons may be sufficient to render it developable. Thus, the quantum efficiency of the overall sequence of events can approach 50%. To understand how such a high value comes about, we n o w examine each of the steps of the Gurney-Mott cycle, discovering what physical properties of the silver halide microcrystal are critical for each. We shall find t h a
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